Nonequilibrium dynamics of optical-lattice-loaded Bose-Einstein-condensate atoms: Beyond the Hartree-Fock-Bogoliubov approximation

Ana Maria Rey, B. L. Hu, Esteban Calzetta, Albert Roura, and Charles W. Clark
Phys. Rev. A 69, 033610 – Published 22 March 2004

Abstract

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose-Einstein condensate selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system. Patterned loading methods may be useful for quantum computing with trapped atoms. This system also serves to illustrate many basic issues in nonequilibrium quantum-field theory pertaining to the dynamics of quantum correlations and fluctuations which goes beyond the capability of a mean-field theory. By numerically evolving in time the initial-state configuration using the Bose-Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atoms and wells. One can also use it to test various approximate methods. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: (a) the Hartree-Fock-Bogoliubov (HFB) approximation, (b) the next-to-leading-order 1N expansion of the 2PI effective action up to second order in the interaction strength, and (c) a second-order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many-body solution for a moderate number of atoms and wells. As a general feature we observe that because the second-order 2PI approximations include multiparticle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution, which a mean-field collisionless approach fails to produce. While the second-order approximations show a clear improvement over the HFB approximation, our numerical results show that they fail at late times, when interaction effects are significant.

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  • Received 13 October 2003

DOI:https://doi.org/10.1103/PhysRevA.69.033610

©2004 American Physical Society

Authors & Affiliations

Ana Maria Rey1,2, B. L. Hu1, Esteban Calzetta3, Albert Roura1, and Charles W. Clark2

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 2Electron and Optical Physics Division, National Institute of Standards and Technology, Technology Administration, U. S. Department of Commerce, Gaithersburg, Maryland 20899-8410, USA
  • 3Universidad de Buenos Aires—Ciudad Universitaria, 1428 Buenos Aires, Argentina

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Vol. 69, Iss. 3 — March 2004

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